Notes on STAR DEATH OVERVIEW There are three ways that a star can end up: as a white dwarf, as a neutron star, or as a black hole. Each of these states is a FINAL state -- that is, once a star is in one of these states, it cannot get out of it (at least not by itself). These three states are considered in chapters 22, 23, and 24 of "Universe", but they are often considered together, as we will do here. In preparing for our second Midterm next week, you will need to know about most of the topics in chapter 22, about half of chapter 23, and only a few basic ideas from chapter 24: Chapter 22 deals with WHITE DWARFS and SUPERNOVAE. We will study both in some detail, including both observed properties (how they are discovered, how they behave, what we can measure) and their physical nature (how they are produced, and why). We will also examine the gaseous remnants that supernovae leave behind, and how these are detected and identified. Chapter 23 deals with PULSARS, which are the stellar remnants left behind when a supernova explodes. These have rather incredible observed properties, giving off pulses of radiation as they rotate with periods of typically one second or less. It has been shown that they must be NEUTRON STARS -- stars composed entirely of neutrons. Indeed, they provide the evidence that neutron stars -- at first a theoretical concept -- actually exist in nature. In this chapter, study sections 1-4 and 9, omitting the more technical sections 5-8. Chapter 24 is about BLACK HOLES, which can be thought of as an application of the ideas of Einstein's General Theory of RELATIVITY. We will not be able to cover this topic properly before the 2nd Midterm (it will be discussed further next week), and so there will be only a few questions on the test dealing with the basic idea of what is meant by the term "black hole", and how they can be detected. If you pick up those basic ideas in class or from these notes, you can put off reading chapter 24 until after the test. WHITE DWARFS Several well-known stars, including Sirius and Procyon, have white dwarf companions. They are so much fainter than the primary components that they are hard to detect, but they have well-known distances (hence absolute magnitudes), and their masses can be found from their gravitational effects on their primaries. In addition, hundreds of single white dwarfs have been found, mostly not very far away. The positions of white dwarfs on the HR diagram tell us their size. Their diameters are only about 1/100 that of the Sun, which means their volumes are only 1/1,000,000 that of the Sun, or about equal to the Earth's. But their masses are comparable to the Sun's, as we know from watching Sirius being swung around by its companion. Thus the density of material in a white dwarf is about one million times that of the Sun. No material known on Earth or produced in a laboratory has a density even close to that. But this is the density reached when a star collapses under gravity, when it no longer has any nuclear energy souces left to draw upon to hold itself up. The production of a white dwarf is described in terms of what happens in the core of a red giant. Following helium burning, the core consists of carbon and oxygen nuclei, but (in small and medium- sized stars like the Sun) the temperature is never high enough to allow these nuclei to fuse. With no nuclear energy sources left, the core collapses until the electrons (which are free particles in this hot gas) refuse to get any closer together. This refusal is the result of the "Pauli exclusion principle", one of the fundamental concepts of quantum mechanics. When this point is reached, we say the gas is "degenerate", and that further collapse is prevented by the pressure of degenerate electrons. Meanwhile, as the core collapses, the star's outer envelope is released, and it expands slowly outward, appearing for a few thousand years as a ring-shaped "planetary nebula", which eventually dissipates. Several hundred planetary nebulae have been catalogued in our Galaxy, and there must be thousands. One of the strange properties of white dwarfs is that the more mass they have, the SMALLER they are. If too much mass is put into a white dwarf, its size goes to zero. In other words, there is a limit to the mass that a white dwarf can have, and this limit turns out to be 1.4 times the mass of the Sun. This is known as the CHANDRASEKHAR LIMIT, after Subrahmanyan Chandrasekhar, the brilliant Indian astrophysicist who figured this out (at the age of 19 -- on his way to college!). He realized that there is a limit to the pressure that degenerate electrons can exert, and hence a limit to the amount of mass that this pressure can hold up. Despite their faintness, many white dwarfs have recently been detected in star clusters -- even distant globular clusters -- confirming the basic ideas of stellar evolution. That is, they account for the stars that are missing from the upper part of the main sequence. Once a white dwarf, always a white dwarf. It has no sources of nuclear energy left, and all it can do is gradually radiate away its heat, getting cooler and fainter. Since the gas is degenerate, its size is held up by electron degeneracy, and it doesn't shrink as it cools off. On the HR diagram, it slides slowly down a line of constant radius. SUPERNOVAE A high-mass star (above 7 or 8 solar masses) has a different ending. In this case the carbon/oxygen core that is produced by helium-burning gets hot enough to fuse, so carbon-burning becomes a new energy source, preventing collapse (temporarily). Then all hell breaks loose. In rapid succession, the burning of carbon, neon, oxygen, and silicon provide energy is successive shells, leading finally to the production of iron at the center. But that's the end of the road, because iron is the most stable of all nuclei, and it is not possible to derive energy from it by either fusion or fission. Now the star no longer has a way to withstand gravity, and the iron core collapses. This is an extremely violent event -- a substantial fraction of all the energy produced by a star in its entire lifetime is released in a few seconds! A flood of neutrinos are released, and shock waves propagate through the outer layers, blowing them off and producing a great deal of radiation. The absolute magnitude goes up to about -18, and then drops gradually over the course of several months. Supernovae are often seen in distant galaxies, attaining a brightness comparable to that of their whole galaxy of billions of stars. They can be seen at such great distances that they are useful for studies of the Universe as a whole, i.e. cosmology. If a supernova went off anywhere in our Galaxy (unless it were behind a thick dust cloud) it would be a bright naked-eye object. In large galaxies like ours, supernovae seem to occur about once in a hundred years, on the average. But the last two supernovae that have been observed in our Galaxy -- Tycho's in 1572 and Kepler's in 1604 -- were recorded before the invention of the telescope! We are overdue! In 1987, a supernova was observed in one of our Galaxy's nearest neighbors, the Large Magellanic Cloud. It was the best-observed supernova ever, although you had to be in the southern hemisphere to see it. At a distance of "only" 51,000 parsecs (165,000 light years), it reached a maximum brightness of 3rd magnitude and was easy to see with the naked eye. It was the first time that a star of known type became a supernova. Surprisingly, it was a blue supergiant, not a red one, before the explosion. But very likely it had already passed through the red supergiant phase. When the supernova SN 1987A occurred, several neutrino detectors at different locations on Earth detected bursts of neutrinos nearly simultaneously. This was the first time that neutrinos had ever been detected from an identifiable astronomical object other than the Sun. They took 165,000 years to get here and all arrived within a few seconds of one another. In the year 1054 A.D., a "guest star" was recorded by astronomers in China, Japan, and Korea, bright enough to be visible in the daytime. Today we know that this was a supernova in our Galaxy, which left a gaseous remnant known as the CRAB NEBULA. Many interesting studies of the Crab (M1) have been done. For example, we can see that it is expanding, at a rate that is consistent with its 950-year age. Its light has two components: a filamentary structure with an emission- line spectrum (thus consisting of excited gas), and an "amorphous" (smooth) component, which has a continuous spectrum. The latter ratiation, at first mysterious, was found to be strongly polarized. It has been interpreted as SYNCHROTRON RADIATION, a type of non-thermal radiation produced by electrons accelerated to very high speeds by magnetic fields, which is also responsible for most of the radiation from radio sources. Indeed, many gaseous remnants of supernovae are bright radio sources, and radio telescopes have contributed greatly to their discovery and interpretation. ANOTHER KIND OF SUPERNOVA We have discussed supernovae that result from the final evolution of a single, massive star. But it turns out that there is another way to make a star explode -- but it requires a pair of stars, orbiting very close to each other. Briefly, if the components of a binary star are sufficiently close to each other, they will affect each other's evolution. The more massive of the two will leave the main sequence first, swelling up to become a red giant. If the components are close enough, they will eventually touch, and matter can be exchanged. After a while, one star becomes a white dwarf, and then the other starts going through its red giant phase. Here is where it starts getting interesting, as matter from the red giant now gets dumped onto the surface of the white dwarf. Two things can happen. The first is what is called an ORDINARY NOVA. Since the surface of a white dwarf is very hot, the only reason that hydrogen fusion is not occurring there is because there's no hydrogen there. But now if you dump hydrogen-rich material from the companion onto the white dwarf, it will fuse. You've just made a hydrogen bomb. The star gets very bright for a while. But this is just a surface explosion, and after a while the star returns to its previous brightness. Years later, the same binary can do it again. Several recurrent novae are known, exploding every 30 years or so. The other thing that can happen is that enough matter is dumped onto the white dwarf to push its mass above the Chandrasekhar limit. That's much more serious, because then the white dwarf is forced to collapse. This is essentially the same as the core collapse of the massive-star supernovae discussed earlier, and the result is the same. This is the other way of producing a supernova, one that doesn't require a massive star. Observationally, the two kinds of supernovae look pretty similar (and they reach similar absolute magnitudes at maximum light), but their light curves and spectra are sufficiently different to allow us to tell them apart. NEUTRON STARS We said there is a limit (1.4 solar masses) to the mass that can hold itself up in the form of a white dwarf. If a star's original mass is less than 5 or 6 solar masses, the mass of the carbon/oxygen core which collapses is under this limit, and it forms a white dwarf (and the rest of the mass is blown away, either gradually over an extended period of time, or in the ejections of planetary nebulae, or both). But if the original mass if great enough, the mass of the collapsing core can exceed the Chandrasekhar limit. What happens then? It will collapse right through the white dwarf configuration -- to what? It was suggested as early as 1934 -- soon after the neutron was discovered -- that such a collapse would create a NEUTRON STAR, a star consisting of nothing but neutrons. The idea is that the negative charges of the electrons and the positive charges of the protons, if pushed together with enough force, would cancel each other out, producing neutrons. Normally, the forces available aren't nearly great enough to do this, but it was suggested that this might happen when a supernova explodes and its core collapses. Indeed, if this happened, the star would collapse down to the point where the neutrons refused to go any closer together. This is another case of the Pauli exclusion principle producing degeneracy, in this case neutron degeneracy, and we say that such a star is held up against gravity by the pressure of degenerate neutrons. Most astronomers didn't pay much attention to this idea -- it sounded sort of crazy, and even if neutron stars existed, they would be so small and faint that they would probably be impossible to detect. Then, suddenly, -- PULSARS were discovered. The first one was found by Jocelyn Bell, using a radio telescope, in 1967. A little pulse of radio energy was recorded every 1.3 seconds, with extreme regularity. It seemed like an artificial signal, but it was coming from a fixed position in the sky. Then another was discovered, then another. Once radio astronomers starting looking for them, quite a few were found. Then in 1970 it was discovered that the radio signal from the Crab Nebula was pulsing at the fantastic rate of 30 times a second. In the same year, strobe techniques were used to study the optical light from the Crab, and it was found that one of the faint stars near the center of the nebula was giving off optical pulses 30 times a second. How can a star do anything as fast as 30 times a second? No star can vibrate that fast, and even a star as dense as a white dwarf can't spin that fast without falling apart. In fact, it was quickly shown that the Crab pulsar must be a neutron star, spinning on its axis 30 times a second. No other kind of star can spin (or do anything) that fast. By implication, other pulsars must also be rotating neutron stars. So within a few years of the discovery of the first pulsar, they were used to demonstrate that neutron stars really do exist in nature. To explain the pulses (after all, a rotating object doesn't necessarily give off pulses) we suppose that the radiation is emitted mostly in a beam, which sweeps around like a searchlight when the star rotates. To explain the beam, we suppose the star has a very strong magnetic field, and that charged particles are ejected along the magnetic axis, giving off synchrotron radiation. This would explain why the pulses are detectable in both optical and radio radiation (and subsequently they've been observed in X-rays, too). The strong magnetic field can be easily accounted for. Ordinary stars like the Sun have detectable magnetic fields and are known to rotate; if such a star were to collapse down to a tiny size, it would rotate much faster and its magnetic field strength would increase enormously. In short, pulsars are rapidly rotating neutron stars. As far as we know, a supernova explosion is the only way they can be produced. Not all supernova remnants have detectable pulsars in them, but several do, and in the other cases it may just be that the beam doesn't ever point towards us as it sweeps around. The pulsar in the Crab Nebula is slowing down. Since it rotates so many times each day, its rotation period is known to incredible accuracy, and changes in its rotation rate were soon detected. The rate of loss of rotational energy could be calculated, and it turned out to be equal to the rate at which the nebula is radiating throughout the spectrum. In other words, the pulsar is the energy source for the nebula -- it is the slowing down of the pulsar's spin that has kept the nebula shining for 950 years! BLACK HOLES Just as there is a limit to the mass of a white dwarf, there must be a limit to the mass of a neutron star. The pressure exerted by degenerate neutrons can only hold up a certain amount of mass. The limiting mass of a neutron star is not well known, but is believed to be just 3 or 4 solar masses. If the collapsing core has more mass than that, it can't become a neutron star. It will collapse further -- to what? This time there is no state of matter that can hold the star up against further collapse, and it will suffer the ultimate collapse, to a state known as a black hole. Einstein realized that light is affected by a gravitational field. A photon follows a curved path when passing close to a massive object, a prediction that was dramatically confirmed during a total eclispe of the Sun in 1919. A photon also loses energy when leaving a gravitating object. Lower energy corresponds to longer wavelength; so if a gravitating object is emitting a spectrum containing spectral lines, an outside observer will see these lines shifted to longer (redder) wavelengths. This is known as the "gravitational redshift". Observationally it is hard to distinguish from the Doppler shift, but it is caused by gravity rather than by motion. The stronger the gravity, the more energy a photon loses, and the greater the redshift. Normally this effect is very small -- for example the gravitational redshift in the solar spectrum, caused by the Sun's gravity, is just barely detectable. But collapsed objects have much stronger gravitational fields, and the effect for neutron stars should be quite large. If you put the same mass into an even smaller volume, the gravitational field goes up still more and the effects get larger. Eventually you reach a point at which a photon loses ALL its energy trying to escape from the gravitational field -- in other words, it doesn't get out. If a massless photon can't get out, nothing can. Then you have what is called a black hole. In principle, a black hole can have any mass. We have seen how a black hole of stellar mass might be produced, by the collapse of a stellar core that is too massive to be supported as a white dwarf or neutron star. Later we will see that much more massive black holes -- containing possibly a million solar masses -- may exist at the centers of galaxies. Very small black holes could also conceivably exist, but we don't know any way for nature to make them. If no radiation (or anything else) can escape from a black hole, how can we possibly detect them? There are several possibilities. First and foremost, they still have gravity and affect their neighbors gravitationally. At some distance away, the effect of their gravity is exactly the same as that of a normal star or anything else of the same mass. Newton's law of gravity still applies. So if one member of a binary star completes its evolution, explodes as a supernova, and produces a black hole, the black hole and its companion will continue orbiting each other. If we detect that the visible star is wobbling, we can in favorable cases determine the mass of the object causing the wobble. If this mass comes out too high to be a white dwarf or neutron star, and if the lack of anything visible rules out an ordinary star of that mass, we may by the process of elimination conclude that the unseen star must be a black hole. Although we cannot receive radiation from inside a black hole, we can detect radiation coming from very close to its surface. Right near the surface of a black hole the conditions are extreme and violent. If there is a disk of gas surrounding the black hole, matter falling into that gas will collide violently with it and heat it to very high temperatures. That would result in the emission of X-rays, which you get whenever you observe gas at temperatures of millions of degrees. Indeed, X-ray satellites have discovered a large number of sources, some of which can be most easily explained in terms of very hot gases close to a collapsed object or black hole. Some of these X-ray sources "flicker" (vary rapidly), which tells us that the X-rays are coming from a very small region. In the case of Cygnus X-1 (the first X-ray source discovered in the constellation Cygnus), all these ideas come together. There is a flickering X-ray source in the direction of a B-type supergiant, which turns out to have a variable radial velocity (i.e. it is a spectro- scopic binary). If the visible star has a normal mass for a B-type supergiant, its unseen companion must have a mass of at least 8 solar masses to cause the observed wobble. It can't be a white dwarf or a neutron star, and an ordinary star of that mass would be bright enough to be easily seen. Evidently the unseen companion is a black hole, and the X-rays come from a hot disk of gas around it. All told, it seems that black holes do really exist. More later. -- Robert Wing February 7, 2001